I'm working on a problem that involves finding the intervals where a function f is increasing and decreasing. Given the function
I worked out that f is increasing on and , and f is decreasing on .
However, the solution in the book claims that f is increasing on [-1,1], rather than [-1,1) like I worked out. I am having trouble understanding why the book claims that this is the case.
I was under the impression that f must be differentiable on the interior of an interval I and continuous on all of I in order to make any statements about increasing/decreasing behavior on the closed interval I. I'm not sure if I am overlooking something, but it seems that f is not continuous on [-1,1]. I would appreciate any clarification.